Solve i=M/c-1/n

$$i = \frac { \frac { M } { c } - 1 } { n }$$

Solve for M

$$M=c\left(in+1\right)$$

$$c\neq 0\text{ and }n\neq 0$$

Solution Steps

Multiply both sides of the equation by n.

$$in=\frac{M}{c}-1$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{c}{c}.

$$in=\frac{M}{c}-\frac{c}{c}$$

Since \frac{M}{c} and \frac{c}{c} have the same denominator, subtract them by subtracting their numerators.

$$in=\frac{M-c}{c}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{M-c}{c}=in$$

Multiply both sides of the equation by c.

$$M-c=inc$$

Add c to both sides.

$$M=inc+c$$

Solve for c

$$\left\{\begin{matrix}c=\frac{M}{in+1}\text{, }&M\neq 0\text{ and }n\neq i\text{ and }n\neq 0\\c\neq 0\text{, }&M=0\text{ and }n=i\end{matrix}\right.$$